Here is a link to a list of articles.  One of them is repair and replacement of Speedo/Tach in a 75 (listed under "Interior"), but I would imagine most of the steps in the removal would be similar if not the same for your 70.  I used these steps before in removing the speedo for my 74.  It was a much bigger job than I thought it would be, but I'm not very mechanically inclined.  manget12008-11-02 14:05:49

http://willcoxcorvette.com/instructions/speedo_W_ser_repair_suggestion.pdf If you tackle it let me know how you make out

I just took my speedometer out of my 78 . Once the dash plastic cover was removed three screws removed and the one speedo cable removed from the back and it was free and clear...but thats a 1978. Corvette specialists of maryland had it back to me in 3 days and just some minor adjustments on the gears and a good cleaning, now fi I can get it back in...

That was fast.

I know on my '76 I will need to lower the steering column when I do my speedo. I do not know if that includes your '70 or not, I think it's '75 to '77.Aaron19762008-11-12 19:28:43

68-77 speedo and tach have to come out from the back of the panel.  They do not come out the front like 78 and up cluster. 6880Mike2008-11-19 08:09:39

Speedo works fine no clicking noise and odometer turns free and clear. Corvette specialist of MD  did it in a very short time . dash all back together.